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<div class="headertitle"><div class="title">windowed_median.cpp File Reference</div></div>
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<div class="contents">
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<p>An implementation of a median calculation of a sliding window along a data stream.
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <cassert></code><br />
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<code>#include <cstdlib></code><br />
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<code>#include <ctime></code><br />
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<code>#include <list></code><br />
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<code>#include <set></code><br />
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<code>#include <vector></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for windowed_median.cpp:</div>
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Classes</h2></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">class  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html">probability::windowed_median::WindowedMedian</a></td></tr>
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<tr class="memdesc:"><td class="mdescLeft"> </td><td class="mdescRight">A class to calculate the median of a leading sliding window at the back of a stream of integer values. <a href="../../df/d34/classprobability_1_1windowed__median_1_1_windowed_median.html#details">More...</a><br /></td></tr>
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Namespaces</h2></td></tr>
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<tr class="memitem:d4/ded/namespaceprobability"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d4/ded/namespaceprobability.html">probability</a></td></tr>
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<tr class="memdesc:d4/ded/namespaceprobability"><td class="mdescLeft"> </td><td class="mdescRight">for <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a> - needed in testing <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:dd/d21/namespacewindowed__median"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../dd/d21/namespacewindowed__median.html">windowed_median</a></td></tr>
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<tr class="memdesc:dd/d21/namespacewindowed__median"><td class="mdescLeft"> </td><td class="mdescRight">Functions for the Windowed Median algorithm implementation. <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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Typedefs</h2></td></tr>
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using </td><td class="memItemRight" valign="bottom"><b>probability::windowed_median::Window</b> = <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/list.html">std::list</a>< int ></td></tr>
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<tr class="separator:aa9dca002d7dfbcaaa68183677a5f0342"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ab5db7d07b43777564ad898d1f8622149"><td class="memItemLeft" align="right" valign="top"><a id="ab5db7d07b43777564ad898d1f8622149" name="ab5db7d07b43777564ad898d1f8622149"></a>
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using </td><td class="memItemRight" valign="bottom"><b>probability::windowed_median::size_type</b> = Window::size_type</td></tr>
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<tr class="separator:ab5db7d07b43777564ad898d1f8622149"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a6dc652a36ea42ba262c4e4236e3e6601"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a> (const <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< int > &vals, int windowSize)</td></tr>
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<tr class="memdesc:a6dc652a36ea42ba262c4e4236e3e6601"><td class="mdescLeft"> </td><td class="mdescRight">namespace probability <a href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">More...</a><br /></td></tr>
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<tr class="separator:a6dc652a36ea42ba262c4e4236e3e6601"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ac0f2228420376f4db7e1274f2b41667c"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d1/ded/windowed__median_8cpp.html#ac0f2228420376f4db7e1274f2b41667c">main</a> (int argc, const char *argv[])</td></tr>
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<tr class="memdesc:ac0f2228420376f4db7e1274f2b41667c"><td class="mdescLeft"> </td><td class="mdescRight">Main function. <a href="../../d1/ded/windowed__median_8cpp.html#ac0f2228420376f4db7e1274f2b41667c">More...</a><br /></td></tr>
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<tr class="separator:ac0f2228420376f4db7e1274f2b41667c"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p >An implementation of a median calculation of a sliding window along a data stream. </p>
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<p >Given a stream of integers, the algorithm calculates the median of a fixed size window at the back of the stream. The leading time complexity of this algorithm is O(log(N), and it is inspired by the known algorithm to [find median from (infinite) data stream](<a href="https://www.tutorialcup.com/interview/algorithm/find-median-from-data-stream.htm">https://www.tutorialcup.com/interview/algorithm/find-median-from-data-stream.htm</a>), with the proper modifications to account for the finite window size for which the median is requested</p>
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<h3><a class="anchor" id="autotoc_md90"></a>
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Algorithm</h3>
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<p >The sliding window is managed by a list, which guarantees O(1) for both pushing and popping. Each new value is pushed to the window back, while a value from the front of the window is popped. In addition, the algorithm manages a multi-value binary search tree (BST), implemented by <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/multiset.html">std::multiset</a>. For each new value that is inserted into the window, it is also inserted to the BST. When a value is popped from the window, it is also erased from the BST. Both insertion and erasion to/from the BST are O(logN) in time, with N the size of the window. Finally, the algorithm keeps a pointer to the root of the BST, and updates its position whenever values are inserted or erased to/from BST. The root of the tree is the median! Hence, median retrieval is always O(1)</p>
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<p >Time complexity: O(logN). Space complexity: O(N). N - size of window </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/YanivHollander" target="_blank">Yaniv Hollander</a> </dd></dl>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="ac0f2228420376f4db7e1274f2b41667c" name="ac0f2228420376f4db7e1274f2b41667c"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#ac0f2228420376f4db7e1274f2b41667c">◆ </a></span>main()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">int </td>
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<td class="paramname"><em>argc</em>, </td>
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</tr>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">const char * </td>
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<td class="paramname"><em>argv</em>[] </td>
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</tr>
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<tr>
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<td></td>
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<td>)</td>
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<td></td><td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Main function. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">argc</td><td>command line argument count (ignored) </td></tr>
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<tr><td class="paramname">argv</td><td>command line array of arguments (ignored) </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
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<p >A few fixed test cases</p>
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<p >Array of sorted values; odd window size</p>
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<p >Array of sorted values - decreasing; odd window size</p>
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<p >Even window size</p>
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<p >Array with repeating values</p>
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<p >Array with same values except one</p>
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<p >Array that includes repeating values including negatives</p>
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<p >Array with large values - sum of few pairs exceeds MAX_INT. Window size is even - testing calculation of average median between two middle values</p>
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<p >Random test cases</p>
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<p >Array size in the range [5, 20]</p>
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<p >Window size in the range [3, 10]</p>
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<p >Random array values (positive/negative)</p>
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<p >Testing randomized test</p>
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<div class="fragment"><div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> {</div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> <span class="comment"></span></div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span><span class="comment"> /// A few fixed test cases</span></div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span><span class="comment"></span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({1, 2, 3, 4, 5, 6, 7, 8, 9}, 3); <span class="comment">/// Array of sorted values; odd window size</span></div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({9, 8, 7, 6, 5, 4, 3, 2, 1}, 3); <span class="comment">/// Array of sorted values - decreasing; odd window size</span></div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({9, 8, 7, 6, 5, 4, 5, 6}, 4); <span class="comment">/// Even window size</span></div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({3, 3, 3, 3, 3, 3, 3, 3, 3}, 3); <span class="comment">/// Array with repeating values</span></div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({3, 3, 3, 3, 7, 3, 3, 3, 3}, 3); <span class="comment">/// Array with same values except one</span></div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({4, 3, 3, -5, -5, 1, 3, 4, 5}, 5); <span class="comment">/// Array that includes repeating values including negatives</span></div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> <span class="comment"></span></div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span><span class="comment"> /// Array with large values - sum of few pairs exceeds MAX_INT. Window size is even - testing calculation of</span></div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span><span class="comment"> /// average median between two middle values</span></div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span><span class="comment"></span> <a class="code hl_function" href="../../d1/ded/windowed__median_8cpp.html#a6dc652a36ea42ba262c4e4236e3e6601">test</a>({470211272, 101027544, 1457850878, 1458777923, 2007237709, 823564440,</div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> 1115438165, 1784484492, 74243042, 114807987}, 6);</div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <span class="comment"></span></div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span><span class="comment"> /// Random test cases</span></div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span><span class="comment"></span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/srand.html">std::srand</a>(<span class="keyword">static_cast<</span><span class="keywordtype">unsigned</span> <span class="keywordtype">int</span><span class="keyword">></span>(<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/chrono/c/time.html">std::time</a>(<span class="keyword">nullptr</span>)));</div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int></a> vals;</div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 8; i < 100; i++) {</div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> <span class="keyword">const</span> <span class="keyword">auto</span> n = 1 + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() / ((RAND_MAX + 5u) / 20); <span class="comment">/// Array size in the range [5, 20]</span></div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <span class="keyword">auto</span> windowSize = 1 + <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/numeric/random/rand.html">std::rand</a>() / ((RAND_MAX + 3u) / 10); <span class="comment">/// Window size in the range [3, 10]</span></div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> vals.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/clear.html">clear</a>();</div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> vals.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/reserve.html">reserve</a>(n);</div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <span class="keywordflow">return</span> 0;</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a6dc652a36ea42ba262c4e4236e3e6601">◆ </a></span>test()</h2>
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<p>namespace probability </p>
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<p >Comparing medians: efficient function vs. Naive one</p>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span><span class="comment"> /// Comparing medians: efficient function vs. Naive one</span></div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span><span class="comment"></span> assert(windowedMedian.getMedian() == windowedMedian.getMedianNaive());</div>
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||||
<g id="edge16" class="edge">
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<title>Node11->Node17</title>
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<path fill="none" stroke="midnightblue" d="M313.05,-114.25C331.56,-90.22 365.22,-51.11 403,-29 410.48,-24.63 419,-21.22 427.44,-18.59"/>
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<polygon fill="midnightblue" stroke="midnightblue" points="428.57,-21.91 437.25,-15.84 426.68,-15.17 428.57,-21.91"/>
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</g>
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</g>
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</svg>
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|
After Width: | Height: | Size: 16 KiB |
Reference in New Issue
Block a user